Best Known (143, 143+40, s)-Nets in Base 3
(143, 143+40, 640)-Net over F3 — Constructive and digital
Digital (143, 183, 640)-net over F3, using
- 1 times m-reduction [i] based on digital (143, 184, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 46, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 46, 160)-net over F81, using
(143, 143+40, 1414)-Net over F3 — Digital
Digital (143, 183, 1414)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3183, 1414, F3, 40) (dual of [1414, 1231, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using
- an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- discarding factors / shortening the dual code based on linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using
(143, 143+40, 96349)-Net in Base 3 — Upper bound on s
There is no (143, 183, 96350)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2057 156166 282517 248324 936671 894557 161407 468388 060123 905450 218286 842465 091028 267110 101161 > 3183 [i]